GATE 2022 MA – Question 48
For max 5x₁+12x₂ subject to x₁+2x₂+x₃≤10,2x₁−x₂+3x₃=8 and x≥0, suppose y=(α,−1)ᵀ is dual feasible. Which must hold?
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Correct answer: (D) α≥7
Explanation
Dual feasibility requires y₁≥0, y₂ unrestricted and Aᵀy≥(5,12,0). Substituting gives α−2≥5,2α+1≥12,α−3≥0. Together these require **α≥7, D**.